Ramseys's Theorem for Pairs (RT^2_2) states that every coloring
of pairs of numbers into two colors (red or blue) has an infinite
homogeneous set A, i.e. pairs of numbers from A all share the same color.
A seemingly weaker version of RT^2_2, the Stable Ramsey's Theorem for
Pairs, states that the same conclusion holds for coloring of pairs with the
additional property that all pairs of numbers with the same first
co-ordinate are eventually all red or blue. In this talk we sketch a
proof of a recent result that over the base theory RCA_0, SRT^2_2 is
strictly weaker than RT^2_2, solving an open problem in reverse
mathematics. This is joint work with Ted Slaman and Yue Yang.